We assume that H_prs, H_p are the groups with the following presentations in the variety of nilpotent groups of class at most two: H_prs = gr(x, y || x^p′ = y^p′ = [x, y]^p = 1), H_p = gr(x, y || [x, y]^p = 1),where p is a prime number, r, s are natural numbers. It is proved that the group H_prs is an absolutely closed group in the quasi-variety qH_prs, and any divisible group belonging to the quasi-variety qH_p is an absolutely closed group in the quasi-variety qH_p.

Key words: quasi-variety, absolutely closed group, dominion, group.